Biomechanical properties of a buzz-pollinated flower

Approximately half of all bee species use vibrations to remove pollen from plants with diverse floral morphologies. In many buzz-pollinated flowers, these mechanical vibrations generated by bees are transmitted through floral tissues, principally pollen-containing anthers, causing pollen to be ejected from small openings (pores or slits) at the tip of the stamen. Despite the importance of substrate-borne vibrations for both bees and plants, few studies to date have characterised the transmission properties of floral vibrations. In this study, we use contactless laser vibrometry to evaluate the transmission of vibrations in the corolla and anthers of buzz-pollinated flowers of Solanum rostratum, and measured vibrations in three spatial axes. We found that floral vibrations conserve their dominant frequency (300Hz) as they are transmitted through the flower, but that vibrations in anthers and petals can gain additional harmonics relative to the pure tone of input vibrations. We also found that vibrations are generally amplified (up to >400%) as they travel from the receptacle at the base of the flower to other floral structures, and that anthers vibrate with a higher amplitude velocity than petals. Together, these results suggest that vibrations travel differently through floral structures and across different spatial axes. As pollen release is a function of vibration amplitude, we conjecture that bees might benefit from applying vibrations in the axes associated with higher vibration amplification.


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Vibrations play an important role in diverse biological interactions from animal communication 23 to predation and pollination [1][2][3]. Communication in invertebrates often occurs through 24 vibrations that are transmitted through the substrate, particularly plant structures [4,5]. For 25 example, male and female wandering spiders use plant leaves to detect each other during pre-26 copulation and some hemipteran predators can detect vibrations produced by leaf-feeding 27 caterpillars during prey search [6,7]. In these cases, substrate properties can affect the 28 vibrations and mediate information transmitted from sender to receiver. To date, our 29 understanding of how plant structures modify the transmission of vibrations is relatively 30 limited [3,5]. 31 Beyond communication, vibrations are also involved in another extraordinary 32 interaction between invertebrates and plants. Some insects, specifically bees, use vibrations to 33 extract pollen grains from certain types of flowers, in a phenomenon called floral buzzing or 34 sonication, which gives rise to the buzz pollination syndrome [8][9][10][11]. Buzz pollination has 35 evolved independently multiple times across flowering plants, being found in more than 65 36 plant families [8,10]. Although the morphology of buzz-pollinated flowers ranges widely 37 [10,12], many buzz-pollinated flowers have repeatedly converged to similar morphologies (e.g. 38 the Solanum-like flower type), with anthers that dehisce through small apical pores (poricidal 39 anthers) arranged in a cone-like central structure, as exemplified by some species in genus 40 Dodecatheon (= Primula, Primulaceae), Miconia (Melastomataceae), Solanum (Solanaceae) 41 and many others [13][14][15]. In buzz-pollinated flowers, mechanical vibrations produced by the 42 thoracic muscles of visiting bees are transmitted to floral tissues resulting in pollen ejection via 43 the apical pores [8,10]. Understanding how bee vibrations are transmitted through different 44 floral structures has the potential to illuminate the mechanistic function of buzz-pollinated 45 flowers while providing the background for further ecological and evolutionary studies of buzz 46 pollination from both bee and flower perspectives. 47 The behaviour of bees while producing floral vibrations is relatively stereotypical 48 [10,12]. Usually, bees land on the flower and use their mandibles and legs to grasp one or 49 multiple stamens, after which they begin rapidly contract their thoracic flight muscles 50 transmitting vibrations to the whole flower [2,16]. Although bees may apply vibrations only to 51 one stamen, pollen can be released from all stamens in the flower simultaneously. This effect 52 is perhaps more dramatically demonstrated in flowers that possess two or more sets of 53 morphologically distinct types of stamens, i.e. they are heterantherous [17][18][19]. In these 54 7 target amplitude values correspond to 20 mm s -1 , 40 mm s -1 and 80 mm s -1 peak amplitude 154 velocity (VPEAK), respectively, and are within the range of floral vibrations measured on flowers 155 during buzz pollination by bumblebees. At a frequency of 300 Hz, these peak velocities 156 correspond to peak accelerations of 37.7 m s -2 , 75.4 m s -2 , and 150.8 m s -2 , and peak 157 displacements of 10. 61 µm, 21.22 µm, and 42.44 µm, respectively (Vallejo-Marín 2019). 158 Vibrations were simultaneously recorded at both receptacle and other flower 159 structures at a sampling frequency of 12,000 samples per second, 781.25 mHz frequency 160 resolution, using a 0-5 kHz bandpass filter, and recorded for 1.28 s. The input vibrations (at the 161 receptacle) could be calibrated very close (± 3 mm s -1 ) to the target amplitude velocities of 162 VRMS = 14 mm s -1 , 28 mm s -1 and 57 mm s -1 (Supplementary Table S1). We played the vibrations 163 at each of the three spatial axes and in each of three amplitude levels in a set of 10 fresh, 164 unvisited S. rostratum flowers (n = 2 recordings x 3 floral structures x 3 axes x 3 amplitudes 165 levels x 10 flowers = 540 vibration recordings). One of the measurements (feeding anther, y-166 axis, input velocity 57 mm s -1 , flower accession 10-s-77-19) was missed during the recording 167 phase and thus not included in the analysis. 168

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The last 300 ms of each recording was used for analysis. The full recording is shown in 170 Supplementary Figure S1. Frequency spectra were estimated using a Hamming window with 171 length of 512 samples and an overlap of 70%. We estimated the dominant frequency and the 172 number of harmonics from the frequency spectra. The number of harmonics was estimated as 173 peaks in the frequency spectrum at multiples of 300 Hz with a relative amplitude of more than 174 10%. We also estimated the VRMS as a measure of vibration amplitude. For this analysis we 175 used the packages seewave [32] and tuneR [33]. 176 We used Poisson linear mixed-effects models implemented in the R package lme4 [34] 177 to compare the number of harmonics on different floral structures. The number of harmonics 178 measured in floral structures were the response variable while floral structure (receptacle, 179 corolla, feeding or pollinating anther) and the axis of measurement (x, y or z) were considered 180 fixed effects. In all models, plant accession (maternal family) was considered a random effect. 181 We compared models with and without the interaction among fixed effects and a null model 182 considering only the random effect using the Akaike information criterion (AIC) [35]. We 183 compared the estimated ΔAIC (the difference between the AIC for the i th model and the 184 minimum AIC among all the models) of each model to choose the best fit. Values of ΔAIC 185 within 0-2 are considered to have substantial support, within 4-7 considerably less support, 186 8 and greater than 10 essentially no support [35]. The AIC as well as other model parameters for 187 comparison were estimated using AICcmodavg [36].The best model was used for parameter 188 estimation of the fixed effects and their interaction assessed using lmerTest [37]. Differences in 189 number of peaks in floral structures were analysed a posteriori using pairwise t-tests with 190 Holm correction [38]. The data were plotted using sciplot [39]. 191 To determine how vibration amplitudes are transmitted to different floral structures, 192 we used linear mixed effects models with Gaussian distribution also implemented in the R 193 package lme4 [34]. In these models, the vibration amplitude velocity (VRMS) measured in the 194 corolla, feeding or pollinating anthers were the response variable. The input amplitude velocity 195 (VRMS) measured at the receptacle, the type of floral structure (corolla, feeding anther or 196 pollinating anther), and the axis of measurement (x, y or z) were considered fixed effects, and 197 plant accession (maternal family) were considered a random effect. We also compared 198 multiple models with and without interactions among fixed effects and the null model only 199 with the random effect using the same AIC methodology described above [35]. Model 200 predictions of the fixed effects in this analyses were plotted using the pred option in sjPlot 201 [40]. All analyses were done in R ver. 3.6.2 (R Core Team, 2020). The code as well as the raw 202 data will be made available upon publication. 203  Table S2 and S3). 212

Frequency of floral vibrations
Although we found more harmonic peaks in anthers than in receptacles in all spatial axes, we 213 found no difference in the number of harmonics between anther types ( Figure 3). The number 214 of harmonics was higher in the corolla than in receptacle only in the x-axis ( Figure 3). 215

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The selected statistical model for amplitude velocity included two-way interactions between 217 input velocity and both floral structure and axis of measurement (Supplementary Table S4 and 218 9 S5). These statistical interactions suggest that differences in amplitude velocity depend on 219 both floral structure and the axis of measurement. The amplitude velocity (VRMS) of vibrations 220 transmitted from the receptacle to the petals closely resembled the input vibration amplitude, 221 showing little evidence of either damping or resonance (Table 1, Figure 4). In contrast, the 222 vibrations transmitted to the tip of both feeding and pollinating anthers were consistently of 223 higher amplitude velocity than the input velocity, revealing amplitude increases that ranged 224 from 69% to 443% (Table 1, Figure 4). The axis with the smallest velocity amplification was the 225 x-axis (69%-110%), while the y-and z-axes showed a higher signal amplification (176%-397% 226 in the y-axis and 229%-443% in the z-axis; Table  during insect communication have also shown preservation of spectral characteristics, which is 245 essential to intra-or inter-specific localisation and recognition [41][42][43]. Interestingly, we found 246 that other floral structures, particularly anthers, show additional harmonics. Multiple 247 harmonics of steeply decreasing amplitude have been recorded in buzz-pollinated flowers 248 [11,29,44,45]. These harmonics also characterise bee vibrations when measured directly on 249 the bee's thorax [46]. Here we have shown that such harmonics arise in floral structures, 250 10 particularly stamens, even when the input vibration is a sinusoidal wave with a pure tone (300 251 Hz). 252 Vibrations including harmonics are expected in some structures including strings and 253 cantilever beams. Interestingly, the two contrasting types of anthers measured presented a 254 similar number of harmonics. Since it is expected that longer and more flexible cantilever 255 beam structures vibrate with a higher number of harmonics [25], we would predict that 256 pollinating anthers have more harmonics than feeding anthers, since the latter are 37% 257 shorter [26,31]. Differences in stiffness between anther types may compensate for the 258 differences in the length of anthers and generate the observed pattern. In other words, our 259 results suggest that the shorter feeding anthers might be more flexible than the longer  Bowers KAW. 1975 The pollinaton ecology of Solanum rostratum (Solanaceae). Am. J. 389 Bot. 62, 633-638. (doi:10.1002/j.1537-2197.1975.tb14094.x) Table   Table 1

Target input VRMS (mm s-1)
Observed VRMS (mm s -1 ) at flower's receptacle  Table S2. Comparison of generalised mixed-effects models with Poisson distribution analysing the number of peaks in the frequency spectrum of floral structures of Solanum rostratum. In all models, number of peaks with a relative amplitude higher than 10% were considered the response variable, and floral structure (str = receptacle, corolla, feeding or pollinating anther) as well as axis of measurement (axes = x, y or z) were considered the fixed effects. Plant accession was considered a random effect. Models were built in a decreasing order of complexity from a full model including interactions. * = interaction; K = number of parameters; AIC = Akaike information criteria; ΔAIC = difference between the AIC for the considered model and the minimum AIC among all the models; Wt = model probabilities; LL = Log Likelihood.